Spatial rigid body dynamics using dual quaternion components

The equations of motion of cooperating robot systems are obtained by connecting the individual equations of motion for each arm and the workpiece using the constraint equations of the closed chain. Dual quaternions have been shown to provide a convenient algebraic representation for these constraints. The equations of motion for a rigid body whose position is defined by the eight dual quaternion coordinates are derived. Because a rigid body has six degrees of freedom, the use of dual quaternion coordinates requires two additional differential constraint equations. The result is a set of ten differential equations prescribing the movement of the body. Use of these equations is demonstrated through a planar example of a double pendulum